MHB Proof of the Division Algorithm

AI Thread Summary
The discussion centers on the application of the well ordering principle (WOP) to subsets of non-negative integers in the context of the division algorithm. It confirms that since any subset of non-negative integers also adheres to the WOP, it is valid to apply the principle in this scenario. The conversation touches on the clarity of the concept, with one participant questioning if their understanding was overly pedantic. Ultimately, the dialogue reflects a light-hearted acknowledgment of occasional confusion regarding mathematical principles. The participants agree on the correctness of applying WOP to non-negative integers.
matqkks
Messages
280
Reaction score
5
In many books on number theory they define the well ordering principle (WOP) as:
Every non- empty subset of positive integers has a least element.
Then they use this in the proof of the division algorithm by constructing non-negative integers and applying WOP to this construction. Is it possible to apply the WOP to a subset of non-negative integers? Am I being too pedantic?
 
Mathematics news on Phys.org
It's rather obvious isn't it? "Applying the WOP to a subset of non-negative integers" would simply mean that, given X, a subset of the non-negative integers, any subset of X has a least member. And that is true because any subset of X is also a subset of the non-negative integers.

If that is not what you mean then please explain what you mean by "apply the WOP to a subset of non-negative integers".​

 
Last edited by a moderator:
Yes of course. I just had a senior moment.
Thanks.
 
There are those of use who live in "senior moments"! We are called "seniors".
 
Last edited by a moderator:

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

I Proof of the Division Algorithm
Replies
3
Views
2K
I Is an algorithm for a proof required to halt?
Replies
3
Views
2K
I Is this proof of the least common multiple theorem in number theory valid?
Replies
1
Views
1K
Insights Fermat's Last Theorem
3
Replies
105
Views
6K
Challenge: Find the minimum amount of draws possible for a list of integers
Replies
9
Views
2K
Why must q be the least element for (q+1)a to be greater than b?
Replies
2
Views
1K
I Fair distribution, minimizing envy
Replies
2
Views
1K
MHB Is There a Mathematical Basis for an Infinite Number of Twin Primes?
Replies
7
Views
4K
I Is the proof of the KRK endgame theorem rigorous and original?
Replies
13
Views
2K
Prove every subset of countable set is either finite or else countable
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top